Social Relations Model:
Estimation Indistinguishable Dyads
David A. Kenny
Strategies
Multilevel
ANOVA
MLM Strategy
Better statistically than the ANOVA
approach
Allows for missing data
One setup for all designs
Can estimate non-saturated models (e.g.,
model with group variances set to zero).
Can more easily estimate the effects of
multiple fixed variables.
With SPSS, HLM
and R’s nlme
Cannot estimate the full SRM.
Must assume
zero actor-partner covariance
positive dyadic reciprocity
With SAS and MLwiN
A method developed by Tom
Snijders
Can estimate the full SRM.
Snijders Approach:
Group Level
Effects can vary at the
group level.
Snijders Approach:
Dyad Level
At the dyad level there are two scores,
one for person A with B and one for
person B with A.
Set these two variances to be equal and
allow for a correlation to measure
dyadic reciprocity.
Advantages
More powerful statistical tests.
Allows for missing data.
Non-saturated models can be
estimated, e.g., a model where
generalized reciprocities are set to
zero.
Easy to estimate effects of covariates.
ANOVA Strategy
Oldest
Uses Expected Mean Squares
Two Major Programs
TripleR
SOREMO
TripleR
Schmukle, Schönbrodt, & Back
http://cran.rproject.org/web/packages/Tripl
eR/index.html
http://www.academia.edu/18037
94/Round_robin_analyses_in_R
_How_to_use_TripleR
TripleR
Schmukle, Schönbrodt, & Back
http://cran.rproject.org/web/packages/Tripl
eR/index.html
http://www.academia.edu/18037
94/Round_robin_analyses_in_R
_How_to_use_TripleR
SOREMO
FORTRAN program originally
written in the early 1980s.
WINSOREMO makes the running
of SOREMO much easier.
Estimation Strategy
Computes estimates of actor,
partner, and relationship
effects.
Computes their variance.
Adjust the variances by irrelevant
components; e.g., variance of
actor effects contains
relationship variance (Expected
Mean Squares)
Getting the Data
Ready
One line per each cell of the design
Ordered as follows:
<1,1>,<1,2>,<1,3>,<1,4>,<2,1> … <4,3>,<4,4>
All variables on that line
Fixed format
Personality variable before dyadic variables
No missing data
Decisions
Same group sizes?
Self data?
Personality variables?
Constructs?
Reverse Variables?
Output
Univariate
Multivariate
Univariate Output
Variance Partitioning
RELATIVE VARIANCE PARTITIONING
VARIABLE
CONTRIBUTE
INFLUENCE
EXHIBIT
CONTROL
PREFER
ACTOR
.335*
.191*
.177*
.242*
.173*
PARTNER RELATIONSHIP
.345*
.320
.443*
.365
.498*
.325
.371*
.386
.270*
.557
Multivariate Output
Matrix: Actor by Actor
ACTOR BY ACTOR
CORRELATION MATRIX
CONTRIBUTE
INFLUENCE
EXHIBIT
CONTROL
PREFER
CONTRIBUTE
1.0000
.7091
.7066
.7559
.6260
INFLUENCE
.7091
1.0000
.6770
.5842
.1728
EXHIBIT
.7066
.6770
1.0000
.6549
.3211
CONTROL
.7559
.5842
.6549
1.0000
.4298
PREFER
.6260
.1728
.3211
.4298
1.0000
Matrices for Actor, Partner, Actor X Partner, Relationship
Intrapersonal, and Relationship Interpersonal
Construct Variance
Partitioning
STABLE CONSTRUCT VARIANCE
VARIABLE
LEADERSHIP
ACTOR
.122
PARTNER
.363
RELATIONSHIP
.132
UNSTABLE CONSTRUCT VARIANCE
VARIABLE
LEADERSHIP
ACTOR
.093
PARTNER
.022
RELATIONSHIP
.267
Anomalous Results with
ANOVA Estimation
Negative Variances
Out-of-range Correlations
Negative Variances
Ordinarily impossible
Happens in SRM analyses
Can treat the variance as if it
were zero.
Out-of-range
Correlations
A correlation greater than +1 or
less than -1.
Two possibilities
Correlation very near one.
Variance due to the component
near zero.
Summary of Results Using
Different Programs
Term
SOREMO SPSS
MLM
Mean
3.868
3.868
3.868
Actor Variance
0.233
0.198
0.198
Partner Variance
0.240
0.192
0.204
Group Variance
-0.091
0.000
0.000
A-P Covariance
0.059
0.000
0.024
Error Variance
0.222
0.237
0.230
Suggested Readings
Appendix B in Kenny’s
Interpersonal Perception (1994)
Kenny & Livi (2009), pp. 174-183
Thank You!